The present invention relates to a method for designing a pneumatic tire, and more particularly, to a method for designing a pneumatic tire capable of efficiently and easily designing the development of a design such as a tire structure, shape, and the like which achieve a single object performance, antinomical performances, and the like.
Conventional methods for designing tires are based on empirical rules achieved by a repetition of numerical experiments using actual experimentation and computers. Therefore, the number of trials and tests required for development is extremely large, which increases development costs, and the development time period cannot be shortened easily.
For example, the shape of the crown portion of a tire is designed on the basis of several arcs in a cross-sectional configuration including a rotational axis of the tire. A value of an arc is determined from data obtained by preparing several molds and testing and evaluating tires prepared from the molds, or is determined by conducting many numerical experiments. Therefore, the development efficiency is not good.
Further, pattern design has many degrees of freedom. Therefore, after grooving a proposed basic pattern in a tire or after actually preparing a mold, a trial tire is made and tested on a vehicle and evaluated. Problems arising at the vehicle are overcome by finely modifying the proposed basic pattern to complete a final pattern. Thus, pattern design is in a field requiring the most processes, as compared with the designing of tire shape and structure.
A pneumatic tire is generally formed with rib grooves in a circumferential direction of the tire and lug grooves in a radial direction of the tire, so as to prevent the hydroplaning phenomenon which is generated during vehicle running in rain, and so as to ensure the braking performance and traction performance. A general pattern is a so-called block pattern which includes island shaped land portions surrounded by these rib grooves and lug grooves.
Such a block pattern requires running performances of the tire, in general, both a straight running performance and a cornering performance. The straight running performance requires a grip force in a circumferential direction of the tire, and a relatively hard rubber is suitable. On the other hand, the cornering performance requires a grip force in a widthwise direction of the tire, and a relatively soft rubber is suitable to increase the grip force during cornering. Due to the soft rubber, there is the need to increase energy loss, which is antinomical.
Therefore, a theoretical approach has recently been made to design a tire which is quiet and safe during running at a high speed on a dry, wet or icy road. Grooves and the like forming the tread of the tire are designed by a plurality of variable pitch repetition design cycles in accordance with a standard which is mathematically calculated. Based on the design values, a tread having land portions divided by lateral grooves and circumferential grooves which define pitches and pitch arrays on the circumference of the tire is obtained. Here, the term xe2x80x9cpitchxe2x80x9d means a relative length of the land portion, and the term xe2x80x9cpitch arrayxe2x80x9d means a sequence of pitches used on the circumference of the tire. A ratio of a pitch length (pitch ratio) may be used as the pitch in some cases.
Each of the pitches may have different length, but in terms of practicality, the lengths are limited to about nine kinds. A particular length of a particular pitch in a given pitch array differs depending upon the circumference of the tire (see Japanese Patent Application Laid-Open No. 4-232105).
However, in many cases, the pitch and pitch array are determined for enhancing the sound performance or for preventing the hydroplaning phenomenon, or are determined by design requirements so as to match the aesthetic sense of the consumer. Further, a plurality of pitches are repeatedly used in the pitch array. Therefore, rigidities are not uniform among land portions of different pitches. Thus, there are problems that uneven wear is increased, and roundness during manufacturing deteriorates.
In view of the above circumstances, it is an object of the present invention to provide a method for designing a pneumatic tire, in which when a plurality of antinomical performances are to be obtained, the best mode of a tire is designed under a given condition, and in which the tire can be efficiently designed and developed.
To achieve the above object, according to an embodiment of the invention, there is provided a method for designing a pneumatic tire including the steps of: (a) determining: a tire basic model including a plurality of different basic shape models representing one shape selected from among a shape of a block alone including an internal structure, a pattern shape of a portion of a tire crown portion including an internal structure, and a shape of a land portion which is continuous in a tire circumferential direction including an internal structure; an objective function representing a tire performance evaluation physical amount; a design variable for determining the shape of the block alone, the pattern shape, or the shape of the land portion; and a constraint condition for restricting at least one of the shape of the block alone, the pattern shape, and the shape of the land portion, and for restricting at least one of a tire cross-sectional shape and the tire performance evaluation physical amount; (b) determining a value of the design variable, until an optimal value of the objective function is obtained, by calculation while varying the value of the design variable and while taking the constraint condition into account; and (c) designing the tire on the basis of the design variable which provides the optimal value of the objective function.
There is also provided in the method for designing a pneumatic tire that the design variable is for determining another shape of the block alone, another pattern shape or another shape of the land portion, by using at least one of the different basic shape models as a reference shape model.
Also provided in the method for designing a pneumatic tire, the shape of the block alone, the pattern shape or the shape of the land portion is determined by using a predetermined basic shape model of the plurality of different basic shape models as a reference model.
There is also provided in the method for designing a pneumatic tire that in the step (b) discussed above, a variation amount of the design variable which provides the optimal value of the objective function while taking the constraint condition into account is estimated based on a sensitivity of the objective function, which is a ratio of a unit variation amount of the design variable to a variation amount of the objective function, and based on a sensitivity of the constraint condition, which is a ratio of a unit variation amount of the design variable to a variation amount of the constraint condition; a value of the objective function when the design variable is varied by an amount corresponding to the estimated amount is calculated and a value of the constraint condition when the design variable is varied by an amount corresponding to the estimated amount is calculated; and a value of the design variable which provides the optimal value of the objective function while taking the constraint condition into account is determined on the basis of the estimated values and the calculated values.
In the method for designing a pneumatic tire discussed above, a selection group including a plurality of tire basic models including a plurality of different basic shape models representing one shape selected from among a shape of a block alone including an internal structure, a pattern shape of a portion of a tire crown portion including an internal structure, and a shape of a land portion which is continuous in a tire circumferential direction including an internal structure is determined; and for each of the tire basic models of the selection group, the objective function, the design variable, the constraint condition, and an adaptive function which can be evaluated from the objective function and the constraint condition are determined; and in the step (b), two tire basic models are selected from the selection group on the basis of adaptive function; design variables of the tire basic models are crossed at a predetermined probability to create a new tire basic model, and/or a portion of the design variable of at least one of the tire basic models is varied to create a new tire basic model; an objective function, a constraint condition and an adaptive function of the tire basic model whose design variable has been varied are determined, the tire basic model and a tire basic model whose design variable has not been whose design variable has been varied are stored, the above operations are repeated until the number of stored tire basic models reaches a predetermined number, it is determined whether a new group including the predetermined number of stored tire basic models satisfies a predetermined convergence condition, and when the convergence condition is not satisfied, the above operations are repeated, by using the new group as the selection group, until the selection group satisfies the convergence condition, and when the convergence condition is satisfied, a value of the design variable which provides the optimal value of the objective function while taking the constraint condition into account is determined from among the predetermined number of stored tire basic models.
There is also provided a method for designing a pneumatic tire, wherein the design variable discussed above includes a variable which represents at least one of: an angle of a surface connected to a surface of the tire land portion which is formed by one shape selected from the shape of the block alone, the pattern shape, and the shape of the land portion; a height to the surface of the tire land portion; a shape of a surface of the tire land portion; a shape of a surface connected to a surface of the tire land portion; a position of a sipe; a number of sipes; a width of a sipe; a depth of a sipe; an inclination of a sipe; a shape of a sipe; and a longitudinal shape of a sipe.
Also provided is a method for designing a pneumatic tire as discussed above, wherein each of the tire basic models including a plurality of basic shape models has a different length in the tire circumferential direction.
Step (a) discussed above determines: a tire basic model including a plurality of different basic shape models representing one shape selected from among a shape of a block alone including an internal structure, a pattern shape of a portion of a tire crown portion including an internal structure, and a shape of a land portion which is continuous in a tire circumferential direction including an internal structure; an objective function representing a tire performance evaluation physical amount; a design variable for determining the shape of the block alone, the pattern shape, or the shape of the land portion; and a constraint condition for restricting at least one of the shape of the block alone, the pattern shape, and the shape of the land portion, and for restricting at least one of a tire cross-sectional shape and the tire performance evaluation physical amount. Each of the block alone including the internal structure, the tire crown portion, and the land portion which is continuous in the tire circumferential direction includes a medium made of single rubber.
The basic shape model representing the shape of the block alone can be formed from a function representing a line which specifies the outer surface shape of the block alone or from a variable representing a coordinate value of an inflection point. The basic shape model representing a pattern shape of a portion of the tire crown portion including an internal structure can be formed from a function which can geometrically analyze the pattern shape at the ground-contacting side of the ground-contacting surface of one land portion of the tire crown portion, e.g., can be formed from a function for determining a polygonal shape such as a rectangular shape or rhombus shape. The basic shape model representing a shape of a land portion which is continuous in the tire circumferential direction including an internal structure can be formed from a function representing a line showing a tire cross-sectional shape or a variable representing the coordinates of an inflection point.
Each of the basic shape models may include at least one of: an angle of a surface connected to a surface of the tire land portion which is formed by one shape selected from the pattern shape and the shape of the land portion; a height to the surface of the tire land portion; a shape of a surface of the tire land portion; a shape of a surface connected to a surface of the tire land portion; a position of a sipe; a number of sipes; a width of a sipe; a depth of a sipe; an inclination of a sipe; a shape of a sipe; and a longitudinal shape of a sipe. Further, as the basic shape model, a model formed by a technique called the finite element method which divides into a plurality of elements may be used, or a model formed by an analytical technique may be used.
The tire basic model includes a plurality of different basic shape models among the basic shape models. For example, in order to design by a plurality of variable pitch repetition design cycles, a tread having land portions which define the pitches and the pitch array on the tire circumference maybe modeled. In this case, a plurality of different pitches are formed on the tire circumference. As the tire basic model, a model by a technique called the finite element method which divides into a plurality of elements may be used, or a model by an analytical technique may be used.
As described above, the tire basic models, i.e., each of the tire basic models having a plurality of basic shape models may have different lengths in a tire circumferential direction. Among tires, there are tires (so-called pitch variation tires) at which land portions are formed on the circumference of the tire at a plurality of different pitches in order to improve the steering stability and quietness. In many cases, in a pitch variation tire, only the length in circumferential direction is varied. Therefore, by using a plurality of basic shape models, in which the lengths in circumferential direction are different, as the tire basic model, it is easy to design a pitch variation tire.
As the objective function representing the performance evaluation physical amount, a physical amount which influences the running performance of the tire such as block rigidity can be used. As the design variable which determines the shape of the block alone or the pattern shape or the shape of the land portion, a variable can be used to determine the pattern, which variable which represents at least one of: an angle of a surface connected to a surface of the tire land portion which is formed by one shape selected from the shape of the block alone, the pattern shape, and the shape of the land portion (i.e., an angle of a block groove wall in the case that a block alone is used); a height to the surface of the tire land portion (i.e., the depth of a groove if a groove is formed); a shape of a surface of the tire land portion; a shape of a surface connected to a surface of the tire land portion; a position of a sipe; the number of sipes; a width of a sipe; a depth of a sipe; an inclination of a sipe; a shape of a sipe; and a longitudinal shape of a sipe. As the constraint conditions, there are the constraint of the tread thickness, the constraint of the block rigidity, the constraint of the angle of the side surface of the land portion formed on the tire (e.g., an angle of a block groove wall in the case that a block alone is used) and the like. The objective function, the design variable and the constraint condition are not limited to the examples described above, and various elements can be used as the objective function, the design variable and the constraint condition in accordance with the purpose of the tire design.
In next step (b), while taking the constraint condition in account, a value of the design variable is obtained by calculation while varying the value of the design variable until an optimal value of the objective function is provided. In this case, it is effective that a variation amount of the design variable which provides the optimal value of the objective function while taking the constraint condition into account is estimated based on a sensitivity of the objective function, which is a ratio of a unit variation amount of the design variable to a variation amount of the objective function, and based on a sensitivity of the constraint condition, which is a ratio of a unit variation amount of the design variable to a variation amount of the constraint condition; a value of the objective function when the design variable is varied by an amount corresponding to the estimated amount is calculated and a value of the constraint condition obtained when the design variable is varied by an amount corresponding to the estimated amount is calculated; and a value of the design variable which provides the optimal value of the objective function while taking the constraint condition into account is determined on the basis of the estimated value and the calculated values. As a result, a value of the design variable when the value of the objective function taking the constraint condition into account is optimal is obtained.
In step (c), the tire is designed by changing the tire basic models on the basis of the design variable which provides the optimal value of the objective function.
Therefore, for a tire basic model including a plurality of different basic shape models, the design variable which provides the optimal value of the objective function, i.e., a selected basic shape model representing the shape of a block alone or a pattern shape or the shape of a land portion, is determined. For example, a shape which is determined by a certain pitch on the tire circumference is obtained, and it is possible to design a tire having uniform rigidities.
The design variable is for determining another shape of the block alone, another pattern shape or another shape of the land portion, by using at least one of the different basic shape models as a reference shape model. By setting in this manner, and by using as a reference the basic shape model which is set as the reference shape model, it is possible to design a tire having uniformized rigidities along such a reference shape model.
Further, the design variable can be set so as to determine the shape of a block alone, a pattern shape or a shape of a land portion by using a predetermined basic shape model as a reference model. By setting in this manner, and by using as a reference the basic shape model which is set as a reference shape model, it is possible to design a tire having uniform rigidities along such a reference shape model. That is, in order to uniformize the rigidities or the like, by setting the basic shape model in advance as an estimated value, and by using as a reference the basic shape model set as the estimated value, it is possible to design a tire having uniform rigidities along the reference shape model.
In the step (a), a selection group including a plurality of tire basic models including a plurality of different basic shape models representing one shape selected from among a shape of a block alone including an internal structure, a pattern shape of a portion of a tire crown portion including an internal structure, and a shape of a land portion which is continuous in a tire circumferential direction including an internal structure is determined; and for each of the tire basic models of the selection group, the objective function, the design variable, the constraint condition, and an adaptive function which can be evaluated from the objective function and the constraint condition are determined.
Next, in the step (b), two tire basic models are selected from the selection group on the basis of the adaptive function; design variables of the tire basic models are crossed at a predetermined probability to create a new tire basic model, and/or a portion of the design variable of at least one of the tire basic models is varied to create a new tire basic model; an objective function, a constraint condition and an adaptive function of the tire basic model whose design variable has been varied are determined, the tire basic model whose design variable has been varied and a tire basic model whose design variable has not been varied are stored, the above operations are repeated until the number of stored tire basic models reaches a predetermined number, it is determined whether a new group including the predetermined number of stored tire basic models satisfies a predetermined convergence condition, and when the convergence condition is not satisfied, the above operations are repeated, by using the new group as the selection group, until the selection group satisfies the convergence condition, and when the convergence condition is satisfied, a value of the design variable which provides the optimal value of the objective function while taking the constraint condition into account is determined from among the predetermined number of stored tire basic models. Based on the value of the design variable which provides the optimal value of this objective function, the tire basic model is changed in step (c), to thereby design the tire.
In this case, in the step (b), for the tire basic model whose design variable has been varied, it is further effective that a variation amount of the design variable which provides the optimal value of the objective function while taking the constraint condition into account is estimated based on a sensitivity of the objective function, which is a ratio of a unit variation amount of the design variable to a variation amount of the objective function, and based on a sensitivity of the constraint condition, which is a ratio of a unit variation amount of the design variable to a variation amount of the constraint condition; a value of the objective function when the design variable is varied by an amount corresponding to the estimated amount is calculated and a value of the constraint condition when the design variable is varied by an amount corresponding to the estimated amount is calculated; the adaptive function is obtained from the value of the objective function and the value of the constraint condition, and the tire basic model and a tire basic model whose design variable has not been varied are stored, and the above operations are repeated until the number of stored tire basic models reaches a predetermined number. With this method as well, it is possible to obtain the value of the design variable in which the value of the objective function becomes optimal while taking the constraint condition into account. As the adaptive function which can be evaluated from the objective function and the constraint condition, a function for determining fitness with respect to the tire basic model from the objective function and the constraint condition can be used. Further, the objective function, the design variable, the constraint condition and the adaptive function are not limited to the above examples only, and various elements can be determined in accordance with the purpose of the tire designing. Further, for crossing the design variables of the tire basic models, there is a method in which portions of design variables of selected two tire models or design variables after a predetermined region are exchanged. Furthermore, for changing a portion of the design variable of the tire basic model, there is a method in which a design variable at a position which is previously determined by probability or the like is changed (mutated).
As described above, according to the present invention, a design variable which provides the optimal value of the objective function while taking the constraint condition into account is determined, and from this design variable, a tire including different block shapes, patterns or the like can be designed. Therefore, unlike the conventional design and development based on trial and error, operations from designing of the best mode to evaluating the performance of the designed tire are made possible to a certain extent mainly by using a computer, efficiency can be remarkably enhanced, the cost of development is reduced, and the block shape or the pattern forming a tire can be designed in accordance with the purpose of use.